Rice, S. O., 1945, “Mathematical Analysis of Random Noise,” Bell Syst. Tech. J., 24 , pp. 45–156.

Stansberg, C. T., 1994, “Second-Order Effects in a Random Wave Modeling,” "*International Symposium: Waves—Physical and Numerical Modeling*", University of British Columbia, Vancouver, Canada, Aug. 21–24, pp. 793–802.

Tick, L. J., 1959, “A Nonlinear Random Model of Gravity Waves (I),” J. Math. Mech., 8 (5), pp. 643–651.

Longuet-Higgins, M. S., 1963, “The Effect of Nonlinearities on Statistical Distributions in the Theory of Sea Waves,” J. Fluid Mech.

[CrossRef], 17 , pp. 459–480.

Hasselmann, K., 1962, “On the Nonlinear Energy Transfer in a Gravity-Wave Spectrum, Part 1, General Theory,” J. Fluid Mech.

[CrossRef], 12 , pp. 481–500.

Sharma, J. N., and Dean, R. G., 1979, “Development and Evaluation of a Procedure for Simulating a Random Directional Second Order Sea Surface and Associated Wave Forces,” Ocean Eng. Rep., 20, University of Delaware.

Huang, N. E., Long, S. R., Tung, C. C., and Yuan, Y., 1983, “A Non-Gaussian Statistical Model for Surface Elevation of Nonlinear Random Wave Fields,” J. Geophys. Res., 88 (C12), pp. 7597–7606.

Tayfun, M. A., 1986, “On Narrow-Band Representation of Ocean Waves,” J. Geophys. Res., 91 (6), pp. 7743–7752.

Martinsen, T., and Winterstein, S. R., 1992, “On the Skewness of Random Surface Waves,” "*Proceedings of the Second ISOPE Conference*"San Francisco, pp. 472–478.

Langley, R. S., 1987, “A Statistical Analysis of Non-Linear Random Waves” Ocean Eng.

[CrossRef], 14 (5), pp. 389–407.

Bouyssy, V., and Rackwitz, R., 1997, “Polynomial Approximation of Morison Wave Loading,” J. Offshore Mech. Arct. Eng., 119 (1), pp. 30–36.

Quek, S. T., Zheng, X. Y., and Moan, T., 2005, “Nonlinear Wave Effects on Distributions of Wave Elevation and Morison Force,” "*Proceedings of the Ninth ICOSSAR Conference*", G.Augusti, G.I.Schuëller, and M.Ciampoli, eds., Millpress, Rotterdam, pp. 3325–3334.

Borgman, L. E., 1969, “Ocean Wave Simulation for Engineering Design,” J. Waterways and Harbors, 95 (4), pp. 557–583.

Zheng, X. Y., and Liaw, C. Y., 2005, “Response Cumulant Spectral Analysis of Linear Oscillators Driven by Morison Forces,” Appl. Ocean. Res.

[CrossRef], 26 (3–4), pp. 154–161.

Stansberg, C. T., 1998, “Non-Gaussian Extremes in Numerically Generated Second-Order Random Waves on Deep Water,” "*Proceedings of the Eighth ISOPE Conference*", Montreal, Canada, pp. 103–110.

Hudspeth, R. T., and Chen, M. C., 1979, “Digital Simulation of Nonlinear Random Waves,” J. Waterways and Harbors, 105 (WW1), pp. 67–85.

Stansberg, C. T., 1993, “Second-order Numerical Reconstruction of Laboratory Generated Random Waves,” "*OMAE Conference*" pp. 143–151.

Zheng, X. Y., and Liaw, C. Y., 2004, “Nonlinear Frequency-Domain Analysis of Jack-Up Platforms,” Int. J. Non-Linear Mech.

[CrossRef], 39 (9), pp. 1519–1534.

Tung, C. C., 1995, “Effects of Free Surface Fluctuation on Total Wave Forces on Cylinder,” J. Eng. Mech.

[CrossRef], 121 (2), pp. 274–280.

Liaw, C. Y., and Zheng, X. Y., 2001, “Inundation Effect of Wave Forces on Jack-Up Platforms,” Int. J. Offshore Polar Eng., 11 (2), pp. 87–92.

Stansberg, C. T., and Gudmestad, O. T., 1996, “Nonlinear Random Wave Kinematics Models Verified Against Measurements in Steep Waves,” "*15th OMAE Conference*", pp. 15–24.

Newland, D. E., 1993, "*Random Vibrations, Spectral and Wavelet Analysis*", Longman Scientific & Technical, New York, Chap. 15.

Forristall, G. Z., 2000, “Wave Crest Distributions: Observations and Second-order Theory,” J. Phys. Oceanogr.

[CrossRef], 30 , pp. 1931–1943.

Zhang, J., Chen, L., Ye, M., and Robert, E. R., 1996, “Hybrid Wave Model for Unidirectional Irregular Waves—Part I. Theory and Numerical Scheme,” Appl. Ocean. Res.

[CrossRef], 18 , pp. 77–92.

Yang, J., and Zhang, J., 2000, “Effects of Wave Intermittency and Nonlinearity on Wave Loads,” "*Proceedings of ETCE/OMAE2000 Joint Conference*", pp. 1–11.

Vinje, T., and Haver, S., 1994, “On the Non-Gaussian Structure of Ocean Waves,” "*Proceedings of the Seventh BOSS Conference*", 2 , MIT, Cambridge, pp. 453–480.

Winterstein, S. R., and Jha, A. K., 1995, “Random Models of Second-order Waves and Local Wave Statistics,” "*Proceedings of the Tenth ASCE Eng. Mech. Specialty Conference*", pp. 1171–1174.

Winterstein, S. R., 1988, “Nonlinear Vibration Models for Extremes and Fatigue,” J. Eng. Mech., 114 , pp. 1772–1790.

Kriebel, D., and Dawson, T. H., 1993, “Nonlinearity in Wave Crest Statistics,” "*Proceedings of the Second International Symposium on Wave Measurement & Analysis, New Orleans*", LA, pp. 61–75.

Hu, S-L. J., 1993, “Nonlinear Random Water Wave,” Book: Computational Stochastic Mechanics, A.H-D.Cheng and C.Y.Yang, eds., Elsevier, New York, pp. 519–543.